Is part of the grease fitting proud of the surface? If so, you may want to try tapping on the fitting (as though driving a nail) to loosen it.
A buddy at work had broken a tap in a blind hole in stainless steel. He's a young guy, I'm the older dude. I let him futz with it for a while, until he gave up. Then I offered to try. Fortunately a little of the tap was still above the surface. It took a good 10 or 15 minutes. Penetrating oil, hammer gently on the broken tap, use a drift punch on one of the exposed flutes to try to turn it and repeat, repeat, repeat. Finally, just as the young guy starts talking about re-making the part, I see the broken tap move, just a little, then a little more, then I chased that little sucker right out of the hole. Chalk one up for the old dude.
Anyway, if you can tap on it, without distorting it, it may, just may, expand the threads in the ball joint ever so slightly, allowing the extractor to extract the broken part of the fitting. Just don't get too heavy handed with the tapping.